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Would this be the case even when the loss function is regularized? Isn't the point of regularization to ensure that the minimum loss corresponds to weights that generalize?
Absolutely not. Regularization seeks to steer optimization toward paths in parameter space that tend to generalize better, but it does not mean that going down to the global minimum would generalize (rather, earlier locations on the path will generalize better compared to no reg)
If that were the case, then you could keep training a regularized network indefinitely and never overfit, only memorizing the right amount of data! Such a regularization technique would be a major breakthrough (see other comment about IB).
François, why do we need to regularize and still have models that are so big they need regularization? Why not just use smaller models and no regularization? (btw, I didn't know you had a book about DL, saw in the other tweet, very nice)
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